Average Error: 3.3 → 3.3
Time: 5.6s
Precision: binary64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[x - x \cdot \left(y \cdot z\right)\]
x \cdot \left(1 - y \cdot z\right)
↓
x - x \cdot \left(y \cdot z\right)
(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))
↓
(FPCore (x y z) :precision binary64 (- x (* x (* y z))))
double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}
↓
double code(double x, double y, double z) {
	return x - (x * (y * z));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.3

    \[x \cdot \left(1 - y \cdot z\right)\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_75733.3

    \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)}\]

  4. Applied distribute-rgt-in_binary64_75303.3

    \[\leadsto \color{blue}{1 \cdot x + \left(-y \cdot z\right) \cdot x}\]

  5. Final simplification3.3

    \[\leadsto x - x \cdot \left(y \cdot z\right)\]

Reproduce

herbie shell --seed 2021014 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))